Can I get a replacement for my lost iPhone using a digital emailed receipt?

Who’s the insurance thru, your carrier? Or do you mean AppleCare+ Theft and Loss?

If AppleCare+ Theft and Loss is it still active? If it is it’s not Apple who does the claim it’s Assurant or AIG you need to speak with.

Look for an email containing an Invoice from no_reply@email.apple.com into your Apple ID email.

You can know it from the invoice you have. The one which was given to you when you made the purchase. If it was from Apple Store you would have received the invoice on your email, provided by you to them while making the purchase.

With online Order Status you can Print an Invoice

Log into Apple

1. Click on the bag icon as shown in the above
2. Click on Sign in
3. Click on Orders
4. Click on the items that you want an invoice for.
5. Click on View Invoice under the Order Number Top right-hand corner. See the pic below...

There you have it.

is there a way I can get a new one or pay to get it replaced?

You would have to ask at the Apple Store, but I imagine that the answer will be "no".

What did the Apple Store tell you when he brought it in?